Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#4712 |
| Fitting | C2×C3×#97 ⋊ C2 |
| Sylow | C3 ⋊ C2×#496 |
668 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(10,11,12,14,13,15,16,17);(6,7,8,9)(11,15)(14,17);(1,2)(4,5)(7,9)(11,14)(12,16)(15,17);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10690115, #10696467, #10696468, … |
| maximal normal subgroup of | #10690115, #10696467, #10696468, … |
| maximal quotient of | C2×#68090, C2×#68091, C2×#68092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11074);